5x^2+8x-4=169

Solution for 5x^2+8x-4=169 equation:

5x^2+8x-4=169

We move all terms to the left:

5x^2+8x-4-(169)=0

We add all the numbers together, and all the variables

5x^2+8x-173=0

a = 5; b = 8; c = -173;
Δ = b2-4ac
Δ = 82-4·5·(-173)
Δ = 3524
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3524}=\sqrt{4*881}=\sqrt{4}*\sqrt{881}=2\sqrt{881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{881}}{2*5}=\frac{-8-2\sqrt{881}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{881}}{2*5}=\frac{-8+2\sqrt{881}}{10}
$